NCERT Solution for Class 8 Maths Rational Numbers
Class 8 Maths Rational Numbers: In mathematics, we usually come across different terms like a natural number, whole numbers, integers, and a rational number. We will discuss a rational number in this article from 8 Class Maths.
Let’s us revisit the properties of Rational numbers in class 8.
Rational Numbers
A rational number is a number that can be written in the form of P/Q where P and Q are integers and Q is not equal to 0.
Example:-5/7, (-2/3)
Properties of Rational numbers
We will first discuss the properties of rational numbers.
Closure Property
We call a set of numbers closed under an operation if performance of that operation on members of the set of numbers always creates a member of the same set only; in this case, we also say that the set is closed under the operation.
Under addition
Rational numbers are closed under addition. For any two rational numbers a and b,a+b is also a rational number.
Under subtraction
Rational numbers are closed under addition. For any two rational numbers a and b, a-b is also a rational number.
Under Multiplication
Rational statistics are closed under multiplication. For any two rational numbers a and b, a*b is also a rational number.
Under Division
Rational numbers are not closed under multiplication. For any rational number a, a/0 is not defined.
Commutative Property
As per commutative property, the interchanging order of numbers will not change the result.
Under addition
Two rational numbers can be added in any order. The addition is commutative for rational numbers. For any two rational numbers a and b, a+b=b+a
Under subtraction
Subtraction is not commutative for rational numbers.
Under Multiplication
Multiplication is commutative for rational numbers. For any two rational numbers a and b, a*b=b*a
Under Division
The division is not commutative for rational numbers
Associative Property
Under addition
The addition is associative for rational numbers. For any 3 rational numbers a,b, and c.
a + (b+c) = (a+b) +c
Under subtraction
Subtraction is not associative for rational numbers
Under Multiplication
Multiplication is associative for rational numbers. For any 3 rational numbers a,b, and c.
a *(b * c) = (a * b) *c
Under Division
The division is not associative for rational numbers.
For illustrations and solved NCERT solutions, visit Class 8 NCERT Maths solutions
The Role of Zero
Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well.
a+0=0+a=a
b+0=0+b=b
The role of 1
1 is the multiplicative identity of rational numbers.
a*1=1*a=a
Negative of a number
For any rational number a/b, we have a/b+(-a/b)=(-a/b)+a/b=0.We say that (-a/b) is the additive inverse of a/b and a/b is the additive inverse of (-a/b).
Reciprocal
A rational number c/d is called the reciprocal or multiplicative inverse of another rational number a/b, if a/b*c/d=1.
Distributive property of multiplication over addition and subtraction
For all rational numbers a,b, and c
a (b+c)=ab+ ac
a(b-c)=ab-ac
Rational Numbers between two rational numbers
Let’s consider the below example for 8th class maths
Q – Find rational number -1/10 and 3/10?
Sol- Rational numbers -1/10 and 3/10 are
0/10,1/10/2/10
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